# VisibleList -- the class of all visible lists

## Description

There are three types of lists that can be entered directly from the keyboard, as follows.
 i1 : {a,b,c} o1 = {a, b, c} o1 : List i2 : [a,b,c] o2 = [a, b, c] o2 : Array i3 : (a,b,c) o3 = (a, b, c) o3 : Sequence
We introduce the class of visible lists as a convenience for referring to lists of these types.

## Types of visible list :

• AngleBarList -- the class of lists delimited by <| ... |>
• Array -- the class of all arrays -- [...]
• List -- the class of all lists -- {...}
• Sequence -- the class of all sequences -- (...)

## Functions and methods returning a visible list :

• "accumulate(Function,Thing,VisibleList)" -- see accumulate -- apply a binary operator repeatedly
• "accumulate(Function,VisibleList)" -- see accumulate -- apply a binary operator repeatedly
• "accumulate(VisibleList,Function)" -- see accumulate -- apply a binary operator repeatedly
• "accumulate(VisibleList,Thing,Function)" -- see accumulate -- apply a binary operator repeatedly
• "flatten(VisibleList)" -- see flatten -- flatten a nested list or a matrix
• "fold(Function,Thing,VisibleList)" -- see fold -- apply a binary operator repeatedly
• "fold(Function,VisibleList)" -- see fold -- apply a binary operator repeatedly
• "fold(VisibleList,Function)" -- see fold -- apply a binary operator repeatedly
• "fold(VisibleList,Thing,Function)" -- see fold -- apply a binary operator repeatedly
• "insert(ZZ,Thing,VisibleList)" -- see insert -- copy a list, inserting an element
• "permutations(VisibleList)" -- see permutations -- produce all permutations of a list
• replace(ZZ,Thing,VisibleList) -- copy a list, replacing an element
• "switch(ZZ,ZZ,VisibleList)" -- see switch -- copy a list, switching two elements
• /// Command \\ Thing /// -- see Thing // Function -- apply a function
• /// Function \\ Thing /// -- see Thing // Function -- apply a function
• "Thing // Command" -- see Thing // Function -- apply a function
• Thing // Function -- apply a function
• "uniquePermutations(VisibleList)" -- see uniquePermutations -- produce all unique permutations of a list
• /// Command \ VisibleList /// -- see VisibleList / Function -- apply a function to elements of a list
• /// Function \ VisibleList /// -- see VisibleList / Function -- apply a function to elements of a list
• "VisibleList / Command" -- see VisibleList / Function -- apply a function to elements of a list
• VisibleList / Function -- apply a function to elements of a list
• VisibleList _ List -- get some entries of a list

## Methods that use a visible list :

• "VisibleList == VisibleList" -- see == -- equality
• between(Thing,VisibleList) -- insert something between elements of a list
• "commonest(VisibleList)" -- see commonest -- the most common elements of a list or tally
• "EXAMPLE(VisibleList)" -- see EXAMPLE -- hypertext EXAMPLE item
• "isSorted(VisibleList)" -- see isSorted -- whether a list is sorted
• "isSubset(Set,VisibleList)" -- see isSubset(Set,Set) -- whether one object is a subset of another
• "isSubset(VisibleList,Set)" -- see isSubset(Set,Set) -- whether one object is a subset of another
• "isSubset(VisibleList,VisibleList)" -- see isSubset(Set,Set) -- whether one object is a subset of another
• length(VisibleList) -- length of a visible list
• "max(VisibleList)" -- see max -- yields the maximum element in a list or sequence
• "member(Thing,VisibleList)" -- see member -- test membership in a list or set
• "min(VisibleList)" -- see min -- yields the minimum element in a list or sequence
• netList(VisibleList) -- a table of boxes
• "numeric(VisibleList)" -- see numeric -- convert to floating point
• "numeric(ZZ,VisibleList)" -- see numeric -- convert to floating point
• "oeis(VisibleList)" -- see oeis -- OEIS lookup
• "part(InfiniteNumber,InfiniteNumber,VisibleList,RingElement)" -- see part -- select terms of a polynomial by degree(s) or weight(s)
• "part(InfiniteNumber,ZZ,VisibleList,RingElement)" -- see part -- select terms of a polynomial by degree(s) or weight(s)
• "part(Nothing,Nothing,VisibleList,RingElement)" -- see part -- select terms of a polynomial by degree(s) or weight(s)
• "part(Nothing,ZZ,VisibleList,RingElement)" -- see part -- select terms of a polynomial by degree(s) or weight(s)
• "part(ZZ,InfiniteNumber,VisibleList,RingElement)" -- see part -- select terms of a polynomial by degree(s) or weight(s)
• "part(ZZ,Nothing,VisibleList,RingElement)" -- see part -- select terms of a polynomial by degree(s) or weight(s)
• "part(ZZ,VisibleList,RingElement)" -- see part -- select terms of a polynomial by degree(s) or weight(s)
• "part(ZZ,ZZ,VisibleList,RingElement)" -- see part -- select terms of a polynomial by degree(s) or weight(s)
• "partition(Function,VirtualTally,VisibleList)" -- see partition -- partition a set or list by values of a function
• "partition(Function,VisibleList)" -- see partition -- partition a set or list by values of a function
• "partition(Function,VisibleList,VisibleList)" -- see partition -- partition a set or list by values of a function
• "position(VisibleList,Function)" -- see position -- the first element of a list satisfying a condition
• "position(VisibleList,VisibleList,Function)" -- see position -- the first element of a list satisfying a condition
• "positions(VisibleList,Function)" -- see positions -- which elements of a list satisfy a condition
• product(VisibleList,Function) -- product of values of a function
• product(VisibleList,VisibleList,Function) -- product of results of applying a function pairwise
• rotate(ZZ,VisibleList) -- rotate a list
• runLengthEncode(VisibleList) -- run length encoding
• Schubert(ZZ,ZZ,VisibleList) -- find the Plücker ideal of a Schubert variety
• "set(VisibleList)" -- see set -- make a set
• "sublists(VisibleList,Function)" -- see sublists -- process interspersed subsequences of a visible list
• "sublists(VisibleList,Function,Function)" -- see sublists -- process interspersed subsequences of a visible list
• "sublists(VisibleList,Function,Function,Function)" -- see sublists -- process interspersed subsequences of a visible list
• "sublists(VisibleList,Function,Function,Nothing)" -- see sublists -- process interspersed subsequences of a visible list
• "sublists(VisibleList,Function,Nothing)" -- see sublists -- process interspersed subsequences of a visible list
• "sublists(VisibleList,Function,Nothing,Function)" -- see sublists -- process interspersed subsequences of a visible list
• "sublists(VisibleList,Function,Nothing,Nothing)" -- see sublists -- process interspersed subsequences of a visible list
• "submatrix'(Matrix,Nothing,VisibleList)" -- see submatrix' -- exclude rows and/or columns of a matrix
• "submatrix'(Matrix,VisibleList)" -- see submatrix' -- exclude rows and/or columns of a matrix
• "submatrix'(Matrix,VisibleList,Nothing)" -- see submatrix' -- exclude rows and/or columns of a matrix
• "submatrix'(Matrix,VisibleList,VisibleList)" -- see submatrix' -- exclude rows and/or columns of a matrix
• submatrix(Matrix,VisibleList) -- select columns
• "submatrix(MutableMatrix,VisibleList)" -- see submatrix(Matrix,VisibleList) -- select columns
• submatrix(Matrix,VisibleList,VisibleList) -- select part of a matrix
• "submatrix(MutableMatrix,VisibleList,VisibleList)" -- see submatrix(Matrix,VisibleList,VisibleList) -- select part of a matrix
• sum(VisibleList,Function) -- sum results of applying a function
• sum(VisibleList,VisibleList,Function) -- sum results of applying a function pairwise
• "tally(VisibleList)" -- see tally -- tally the elements of a list, sequence, array, or string
• "unique(VisibleList)" -- see unique -- eliminate duplicates from a list
• /// SelfInitializingType \ VisibleList /// -- see VisibleList / Function -- apply a function to elements of a list
• "VisibleList / SelfInitializingType" -- see VisibleList / Function -- apply a function to elements of a list
• VisibleList _ ZZ -- get element from list

## For the programmer

The object VisibleList is a type, with ancestor classes BasicList < Thing.